Dynamic positron emission tomography (PET) imaging provides a non-invasive means of estimating kinetic model parameters characterizing tracer uptake~ such quantitative information is important to understand physiological processes and to optimize clinical scan protocols for disease diagnosis and treatment monitoring. The conventional approach to perform dynamic PET is to acquire a series of independent time frames, reconstruct individual time frame images, and generate voxel- or region-wise radioactivity curves over time (time activity curves, TACs). These TACs are fitted with a relevant kinetic model with standard curve-fitting methods to estimate kinetic parameters. An alternative method is to directly reconstruct images of the kinetic parameters from raw data without explicitly defining a framing sequence. Because the noise distribution is better characterized in the raw data than in reconstructed time frame images and no temporal resolution is lost to framing, direct reconstruction yields parameter estimates with a higher signal-to-noise ratio (SNR). However, when parametric images are directly reconstructed using a single model across the entire field-of- view, errors arising from voxels with poor model conformity can propagate spatially. This is prevalent in non- brain imaging, as multiple kinetic behaviors are typically present in the field-of-view. The goal of the proposed research is to develop a hybrid direct reconstruction algorithm that combines parametric and non-parametric models to accommodate heterogeneous kinetics without the spatial error propagation observed in more basic direct approaches. The application of interest is the estimation of myocardial blood flow from cardiac PET with rubidium-82, for which the myocardial tissue time activity curve is assumed to adhere to a one-tissue (1T) compartmental model with spillover correction terms, while the remainder of the field-of-view does not. Because SNR in PET suffers with low counts, a direct reconstruction approach is particularly desirable for such an application due to the short half-life of rubidium-82, 76 seconds. Voxels designated as belonging to the myocardium will be modeled with 1T kinetics~ the remaining voxels will be modeled with cubic B-spline curves. The significance of the proposed hybrid 4D PET reconstruction algorithm is the potential to administer a lower dose of radiation while maintaining a given SNR, and to improve the SNR in inherently low-count applications. Another development to be explored is the simultaneous estimation of the arterial input function in conjunction with the kinetic parameters. The input function is a critical component of the compartmental model, and must either be measured invasively with arterial sampling or derived from the image data, e.g. by segmenting the left ventricle and obtaining its time activity curve from a series of reconstructed time frames. By including the input function estimation in the direct reconstruction, both of these more tedious alternatives could be avoided, potentially with less noise and higher accuracy.